Elegant way to invert a map in Scala

Question

Learning Scala currently and needed to invert a Map to do some inverted value->key lookups. I was looking for a simple way to do this, but came up with only:

Answer 1

I came here looking for a way to invert a Map of type Map[A, Seq[B]] to Map[B, Seq[A]], where each B in the new map is associated with every A in the old map for which the B was contained in A's associated sequence.

E.g.,
Map(1 -> Seq("a", "b"), 2-> Seq("b", "c"))
would invert to
Map("a" -> Seq(1), "b" -> Seq(1, 2), "c" -> Seq(2))

Here's my solution :

val newMap = oldMap.foldLeft(Map[B, Seq[A]]().withDefaultValue(Seq())) {
  case (m, (a, bs)) => bs.foldLeft(m)((map, b) => map.updated(b, m(b) :+ a))
}

where oldMap is of type Map[A, Seq[B]] and newMap is of type Map[B, Seq[A]]

The nested foldLefts make me cringe a little bit, but this is the most straightforward way I could find to accomplish this type of inversion. Anyone have a cleaner solution?